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A132993 Triangle t(n,m) = P(n-m+1) * P(m+1) read by rows, 0<=m<=n, where P=A000041 are the partition numbers.

%I A132993 #8 Sep 17 2015 03:02:01
%S A132993 1,2,2,3,4,3,5,6,6,5,7,10,9,10,7,11,14,15,15,14,11,15,22,21,25,21,22,
%T A132993 15,22,30,33,35,35,33,30,22,30,44,45,55,49,55,45,44,30,42,60,66,75,77,
%U A132993 77,75,66,60,42,56,84,90,110,105,121,105,110,90,84,56
%N A132993 Triangle t(n,m) = P(n-m+1) * P(m+1) read by rows, 0<=m<=n, where P=A000041 are the partition numbers.
%e A132993 1;
%e A132993 2, 2;
%e A132993 3, 4, 3;
%e A132993 5, 6, 6, 5;
%e A132993 7, 10, 9, 10, 7;
%e A132993 11, 14, 15, 15, 14, 11;
%e A132993 15, 22, 21, 25, 21, 22, 15;
%e A132993 22, 30, 33, 35, 35, 33, 30, 22;
%e A132993 30, 44, 45, 55, 49, 55, 45, 44, 30;
%e A132993 42, 60, 66, 75, 77, 77, 75, 66, 60, 42;
%e A132993 56, 84, 90, 110, 105, 121, 105, 110, 90, 84, 56;
%p A132993 A132993 := proc(n,m)
%p A132993         combinat[numbpart](n-m+1)*combinat[numbpart](m+1) ;
%p A132993 end proc:
%p A132993 seq(seq(A132993(n,k),k=0..n),n=0..12) ; # _R. J. Mathar_, Nov 11 2011
%t A132993 << DiscreteMath`Combinatorica`; << DiscreteMath`IntegerPartitions`; Clear[t, n, m]; t[n_, m_] = PartitionsP[n - m + 1]*PartitionsP[m + 1]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
%Y A132993 Cf. A000041, A048574 (row sums).
%K A132993 nonn,tabl
%O A132993 0,2
%A A132993 _Roger L. Bagula_ and _Gary W. Adamson_, Aug 27 2008